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February, 1994 The Trouble with Diversity: Fork-Join Networks with Heterogeneous Customer Population
Vien Nguyen
Ann. Appl. Probab. 4(1): 1-25 (February, 1994). DOI: 10.1214/aoap/1177005198

Abstract

Consider a feedforward network of single-server stations populated by multiple job types. Each job requires the completion of a number of tasks whose order of execution is determined by a set of deterministic precedence constraints. The precedence requirements allow some tasks to be done in parallel (in which case tasks would "fork") and require that others be processed sequentially (where tasks may "join"). Jobs of a given type share the same precedence constraints, interarrival time distributions and service time distributions, but these characteristics may vary across different job types. We show that the heavy traffic limit of certain processes associated with heterogeneous fork-join networks can be expressed as a semimartingale reflected Brownian motion with polyhedral state space. The polyhedral region typically has many more faces than its dimension, and the description of the state space becomes quite complicated in this setting. One can interpret the proliferation of additional faces in heterogeneous fork-join networks as (i) articulations of the fork and join constraints and (ii) consequences of the disordering effects that occur when jobs fork and join in their sojourns through the network.

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Vien Nguyen. "The Trouble with Diversity: Fork-Join Networks with Heterogeneous Customer Population." Ann. Appl. Probab. 4 (1) 1 - 25, February, 1994. https://doi.org/10.1214/aoap/1177005198

Information

Published: February, 1994
First available in Project Euclid: 19 April 2007

zbMATH: 0797.60078
MathSciNet: MR1258171
Digital Object Identifier: 10.1214/aoap/1177005198

Subjects:
Primary: 60K25
Secondary: 60F17 , 60J65 , 90B30

Keywords: diffusion approximations , Fork-join networks , heavy traffic analysis , heterogeneous customer populations , nonsimple polyhedral state space , reflected Brownian motion

Rights: Copyright © 1994 Institute of Mathematical Statistics

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Vol.4 • No. 1 • February, 1994
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